Linear kinetic theory of instabilities of a gravitatingstellar disk

Abstract

Linear kinetic theory is developed to describe collective oscillations (and their instabilities) propagating in a rapidly rotating disk of stars, representing a highly flattened galaxy. The analysis is carried out for the special case of a self-gravitating, infinitesimally thin, and spatially inhomogeneous system, taking into account the effects both of thermal movements of stars and of gravitational encounters between stars and giant molecular clouds of an interstellar medium. The star–cloud encounters are described with the use of the Landau collision integral. The dynamics of gravity perturbations with rare interparticle encounters is considered. Such a disk is treated by employing the well elaborated mathematical formalisms from plasma perturbation theory using normal-mode analysis. In particular, the method of solving the Boltzmann equation is applied by integration along paths, neglecting the influence of star–cloud encounters on the distribution of stars in the zeroth-order approximation. We are especially interested in important kinetic effects due to wave–star resonances, which we have little knowledge about. The kinetic effects are introduced via a minor drift motion of stars which is computed from the equations of stellar motion in an unperturbed central force field of a galaxy. The dispersion laws for two main branches of disk's oscillations, that is the classical Jeans branch and an additional gradient branch, are deduced. The resonant Landau-type instabilities of hydrodynamically stable Jeans and gradient gravity perturbations is considered to be a long-term generating mechanism for propagating density waves, thereby leading to spiral-like and/or ring-like patterns in the flat galaxies.